Question

1. simplify an expression for the perimeter of the rectangle. image of a rectangle with width labeled 3w and height labeled 5w - 2 perimeter: _

Explanation:

Step1: Recall perimeter formula for rectangle

The formula for the perimeter \( P \) of a rectangle is \( P = 2\times(\text{length} + \text{width}) \). Here, the length is \( 5w - 2 \) and the width is \( 3w \).

Step2: Substitute values into the formula

Substitute length and width into the formula: \( P = 2\times((5w - 2) + 3w) \).

Step3: Simplify inside the parentheses

Combine like terms inside the parentheses: \( (5w - 2) + 3w = 5w + 3w - 2 = 8w - 2 \).

Step4: Multiply by 2

Multiply the simplified expression by 2: \( P = 2\times(8w - 2) = 2\times8w - 2\times2 = 16w - 4 \).

Answer:

\( 16w - 4 \)